Authors: Franke, Brice
Wendler, Martin
Title: Stable limit theorem for U-statistic processes indexed by a random walk
Language (ISO): en
Abstract: Let (Sn)n2N be a random walk in the domain of attraction of an a -stable Lévy process and ( (n))n2N a sequence of iid random variables (called scenery). We want to investigate U-statistics indexed by the random walk Sn, that is Un := P 1 i<j n h( (Si); (Sj )) for some symmetric bivariate function h. We will prove the weak convergence without the assumption of finite variance. Additionally, under the assumption of finite moments of order greater than two, we will establish a law of the iterated logarithm for the U-statistic Un.
Subject Headings: law of the iterated logarithm
random scenery
random walk
stable limits
Issue Date: 2012-12-17
Appears in Collections:Sonderforschungsbereich (SFB) 823

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